Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C3×C5×C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #416 |
| Sylow | C5 ⋊ #5113 |
| Sylow | C3 ⋊ #65402 |
316 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|b^2=f,c^2=de,d^2=f,c^a=cd,d^a=df,g^a=g^2,h^a=h^4252 conjugacy classes — view the full character table.
| maximal subgroup of | #14295906, #14295909, #14295957, … |
| maximal normal subgroup of | #14295906, #14295909, #14295957, … |
| maximal quotient of | #14281568, #14281866, #14282164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5409);